Algorithms for Wireless Sensor Networks

Marcela Boboila, George Iordache

Computer Science Department

Stony Brook University

Presented paper

[Li05] Zang Li, Wade Trappe, Yanyong Zhang, Badri Nath, Robust statistical methods for securing wireless localization in sensor networks, IPSN’05

The problem

Location based services are exposed to malicious attacks

=> design localization algorithm that are robust to corrupted measurements

Not concerned with accidental anomalies (i.e. open a door, someone passing by), but with intelligent, coordinated attacks

Attacks in wireless localization

Attacks in wireless localization

Approach

Mitigate the vulnerabilities instead of introducing countermeasures for every possible attack

“Live with bad nodes instead of eliminating all possible bad nodes”

Proposed solutions

Triangulation-based localization: Solution: switch from least squares (LS)

estimation to least median squares (LMS) when attacked

RF-based fingerprinting localization: Solution: use a median-based distance metric

Triangulation – Least Squares (LS) Method Gather a collection of (x, y, d)

d = the distance from the wireless device to an anchor (x, y)

Map values on a parabolic surface:

minimum is the wireless device location

Resolve an overdetermined system, for which we know and we determine

Triangulation - attack

An intruder can perturb the distance d (i.e. alters hop count)

A single perturbation can alter the result

General formulation of the LS

N = total number of samples

θ = the parameter to estimate (location)

corresponds to

corresponds to position (xi, yi) of the anchors

Solution: Least Median of Squares (LMS)

The LMS estimator [P. J. Rousseeuw ’84] is among the most widely used robust linear statistical estimators

The residue from LS:

Minimize the medium of the residue squares:

LMS algorithm

• Choose a number of M subsets of size n from the N samples

• Applying LS, find the estimate , j=1,...,M for each subset

• Based on the median residual error assign a weight for each (i.e. weight=1 if the error is less than a threshold, or 0 otherwise)

• Compute weighted estimated

LMS algorithm

• LS – no attack:

• LMS – attack:

How choose n and M for LMS?

Idea: at least one subset is “good” (no contamination) with probability:

ε = contamination ratio => εN samples are outliers

n=4 (3 would be minimum to decide a location)

M=20 (depends on computational capabilities)

P>=0.99

ε <=30%

How to get a location estimate from samples efficiently?

Nonlinear LS: Linear LS:

How to get a location estimate from samples efficiently?

Use linear LS – reduces computational complexity

Simulations

The strength of the attack:

N = 30 anchor nodes, 500 x 500 m2 region

Simulations

LMS: the error increases to a maximum, then decreases slightly and then stabilizes

At low attacking strength, LS performs better than LMS With high contamination ratios, the system performs poorly

Simulations

Why LS performs better than LMS at low attacking strength? linear regression: LMS detects well only when

outlier and inlier are well separated

Simulations

The variance indicates the distance between inliers and the outliers

Establish threshold T If the variation (variance expansion due to

outliers) > T, then apply LMS, else apply LS

Proposed solutions

Triangulation-based localization: Solution: switch from least squares (LS)

estimation to least median squares (LMS) when attacked

RF-based fingerprinting localization: Solution: use a median-based distance metric

RF-based fingerprinting RADAR system – in buildings

How it works: Setup phase: form a radio map with signal strengths

(fingerprints) a mobile host broadcasts to base stations records are written in radio map on central base station

and they have the format described below:

(x, y) – mobile position - received signal strength at the ith base station

Localization phase: nearest neighbor in signal space (NNSS)

RF-based fingerprinting - attack

Corrupted signal strength at one base station (i.e. insert an absorbing barrier between mobile host and base station)

Solution: use the median distance “nearest” neighbor:

minimize

Observations

What the paper does: Logical, well-structured paper, strengthened by graphical

results Makes a classification of possible attacks in wireless

sensor networks Employs previously developed statistical methods to

minimize the effect of adversaries in the localization process, instead of eliminating it

Proposes a lower-computational method (LMS), in comparison with a previous, related one (LS). The reduction in computational demands suggests that this method can be better integrated in sensor networks

Observations

What the paper does not: It doesn’t study the effect over the whole system when the

method is applied: computational complexity, energy consumption, feasibility,

time for algorithm completion Doesn’t study a broader range of undesired interferences:

arbitrary interferences with the signal information (weather conditions, etc.)

accidental or malicious movement of sensors in places out of the scope of the application

Not original - it adapts a method (LMS) which has already been applied in different areas (security, etc.) (see references)

Observations

How to strengthen the paper: Comparison with other methods used to secure

the localization process in sensor networks Results showing how well the global localization

algorithm (more nodes, not only one, need to determine their position ) performs

Results indicating overall energy consumption, computation, time costs, etc.

Instead of simulation, employ a real situation